5. A population P of bacteria grows at a rate (say b.P , b > 0) proportional to its size, but it is destroyed at a stead
Posted: Tue Sep 07, 2021 7:46 am
5. A population P of bacteria grows at a rate (say b.P , b > 0) proportional to its size, but it is destroyed at a steadily increasing rate (say cit, c > 0) by a spot of mold which starts growing at t = 0. Under what circumstances will the mold completely consume the bacteria ? Hint. Solve P' (t) = bP(t) – ct in terms of b, c, P(0) and t. Under what condition(s) (on P(0), b and c) will P(t) drop to zero for some t > 0 ?